What can asymptotic expansions tell us about large-scale quasi-geostrophic anticyclonic vortices? - Archive ouverte HAL Access content directly
Journal Articles Nonlinear Processes in Geophysics Year : 1995

What can asymptotic expansions tell us about large-scale quasi-geostrophic anticyclonic vortices?

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Abstract

The problem of the large-scale quasi-geostrophic anticyclonic vortices is studied in the framework of the baratropic rotating shallow- water equations on the ß-plane. A systematic approach based on the multiplescale asymptotic expansions is used leading to a hierarchy of governing equations for the large-scale vortices depending on their characteristic size, velocity and a free surface elevation. Among them are the Charney-Obukhov equation, the intermediate geostrophic model equation, the frontal dynamics equation and some new nonlinear quasi-geostrophic equation. We are looking for steady-drifting axisymmetric anticyclonic solutions and find them in a consistent way only in this last equation. These solutions are soliton-like in the sense that the effects of weak non-linearity and dispersion balance each other. The same regimes on the paraboloidal ß-plane are studied, all giving a negative result in what concerns the axisymmetric steady solutions, except for a strong elevation case where any circular profile is found to be steadily propagating within the accuracy of the approximation.
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Dates and versions

hal-00331036 , version 1 (01-01-1995)

Identifiers

  • HAL Id : hal-00331036 , version 1

Cite

A. Stegner, V. Zeitlin. What can asymptotic expansions tell us about large-scale quasi-geostrophic anticyclonic vortices?. Nonlinear Processes in Geophysics, 1995, 2 (3/4), pp.186-193. ⟨hal-00331036⟩
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